Hi,
Some shipping methods are ok with just the weight. Some others also require the dimensions. So, at least until you get shipping methods to display on the checkout, it's best to try with a product which has both.
We don't need the username/password, you can blur them on the screenshots. We need to see all the other options of the shipping method.
Regarding the taxes, the problem probably comes from:
Copied the United States of America data from the countries to the tax zones.
I'm not sure what you mean, by that, but there is no copying to do. You're supposed to directly select the country zone "United States of America" in the zone setting of your tax rule. If you created another zone with the same name and used it instead of the country zone, then it explains the issue: the country zone selected in the address of the user is not linked to the zone you created for your tax rule and thus the tax rule doesn't apply.